小扰动下奇异闭轨附近后继函数的光滑性  

The Smoothness of Successor Function in the Neighborhood of the Singular Cycle of the Perturbated System

作　　者：丰璐[1] 孙立建[2] 

机构地区：[1]天津财经大学数学系,天津300222 [2]天津科技大学数学系,天津300457

出　　处：《南昌大学学报（理科版）》2008年第4期320-326,共7页Journal of Nanchang University(Natural Science)

基　　金：天津市哲学社会科学研究规划资助项目(TJYY07-1-17)

摘　　要：扰动系统在奇异闭轨附近的后继函数对于判断奇异闭轨分支出极限环的个数、极限环的稳定性和相对位置具有极其重要的作用。通过对Dulac映射及正则映射的光滑性的研究得到结论:具有奇异闭轨的Ck系统在小扰动下奇异闭轨附近的的后继函数为Ck-1的。所得结果简洁,可为以后相关研究工作的开展提供方便。It is very important for successor function to judge the number, the stability and the relative place of the limit cycles of the perturbated system. In this paper,the smoothness of successor function in the neighborhood of the singular cycle of the perturbated system has been studied by analyzing the smooth＇ quality of Dulac mapping and regular mapping, and got the main conclusion： The successor function in the neighborhood of the perturbated singular system is C^k-1 , when the system is C^k. The result is concise and convenient,. It can reduce quality condition of planar system in the many theories.

关 键 词：奇异闭轨 Dulac映射 正则映射 后继函数 光滑性 

分 类 号：O175.13[理学—数学]